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A063495 a(n) = (2*n-1)*(5*n^2-5*n+2)/2. 17

%I

%S 1,18,80,217,459,836,1378,2115,3077,4294,5796,7613,9775,12312,15254,

%T 18631,22473,26810,31672,37089,43091,49708,56970,64907,73549,82926,

%U 93068,104005,115767,128384,141886,156303,171665,188002,205344

%N a(n) = (2*n-1)*(5*n^2-5*n+2)/2.

%H Harry J. Smith, <a href="/A063495/b063495.txt">Table of n, a(n) for n=1..1000</a>

%H T. P. Martin, <a href="http://dx.doi.org/10.1016/0370-1573(95)00083-6">Shells of atoms</a>, Phys. Rep., 273 (1996), 199-241, eq. (10).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).

%F From _Harvey P. Dale_, Dec 18 2011: (Start)

%F a(1)=1, a(2)=18, a(3)=80, a(4)=217, a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) - a(n-4).

%F G.f.: (x^3+14*x^2+14*x+1)/(1-x)^4. (End)

%F E.g.f.: (-2 + 4*x + 15*x^2 + 10*x^3)*exp(x)/2 + 1. - _G. C. Greubel_, Dec 01 2017

%t Table[(2n-1)(5n^2-5n+2)/2,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,18,80,217},40] (* _Harvey P. Dale_, Dec 18 2011 *)

%o (PARI) { for (n=1, 1000, write("b063495.txt", n, " ", (2*n - 1)*(5*n^2 - 5*n + 2)/2) ) } \\ _Harry J. Smith_, Aug 23 2009

%o (PARI) x='x+O('x^30); Vec(serlaplace((-2+4*x+15*x^2+10*x^3)*exp(x)/2 + 1)) \\ _G. C. Greubel_, Dec 01 2017

%o (MAGMA) [(2*n-1)*(5*n^2-5*n+2)/2: n in [1..30]]; // _G. C. Greubel_, Dec 01 2017

%Y 1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 01 2001

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Last modified February 18 17:08 EST 2018. Contains 299325 sequences. (Running on oeis4.)